ow long would a DV divorce case take if my husband refused to sign papers?

I was looking into filing for a domestic violence divorce. HI do have two small children but the children are not biologically his. I have full sole custody of both of my children. We don't have any property that we own together, no cars etc. I would like to get divorce as quickly as possible so that I can finally move on with my life. Also, he was arrested and was charged with simple assault and I do have court papers for that.